Karl-Franzens-University Graz

Institute of Physics

Master Thesis

Adsorption of Oligoacenes

and Their Derivatives on Metal Surfaces:

A Density Functional Study

AuthorMartin Unzog

SupervisorProf. Peter Puschnig

Graz, May 7, 2019

ii

Abstract

In this thesis we investigate oligoacaenes and their derivatives on metal surfacesby means of density functional theory (DFT). In the first chapter we review den-sity functional theory and how it is used in practice. There, we also discuss topicswhich come up often in this thesis: the workfunction and its changes, the projecteddensity of states, simulation of photoemission tomography maps and finally the the-ory of scanning tunneling microscopy (STM). In the second chapter we investigatefour different adsorption geometries of tetracene on Ag(110). For each of those ge-ometries we investigate the electronic structure by calculating the workfunction, therespective workfunction change and the projected density of states. For two of thosegeometries we simulate angle-resolved photoemission maps using the one-step modeland compare them with experimentally available maps. In the second chapter we in-vestigate dihydrotetraazapentacene on Cu(110)-(2x1)O. We determine the optimaladsorption site by first locally relaxing the molecules on different adsorption sitesand then comparing the energies of the relaxed geometries. Furthermore we calcu-late the diffusion barrier between two adjacent optimal adsorption sites. We alsosimulate STM images for these different geometries by using the Tersoff-Hamannapproximation and compare the simulated STM image of the optimal adsorptiongeometry with experimentally available STM data.

iii

iv

Kurzzusammenfassung

In dieser Masterarbeit untersuchen wir mit Hilfe der Dichtefunktionaltheorie (DFT)Oligoazene und deren Derivate auf Metalloberflachen. Im ersten Kapitel verschaffenwir uns einen Uberblick uber die Dichtefunktionaltheorie und wie sie in der Praxisangewendet wird. Dort werden wir auch Themen diskutieren, die oft in der Master-arbeit vorkommen werden: die Austrittsarbeit und deren Anderung, die projizierteZustandsdichte, die Simulation von Photoemissions-Tomografie-Karten und zuletztdie Theorie der Rastertunnelmikroskopie (RTM). Im zweiten Kapitel untersuchenwir vier verschiedene Adsorptionsgeometrien von Tetrazen auf Ag(110). Fur jededieser Geometrien untersuchen wir die elektronischen Eigenschaften, indem wir dieAustrittsarbeit, deren jeweilige Anderung und die projizierte Zustandsdichte berech-nen. Fur zwei dieser Geometrien simulieren wir mit dem ”one-step” Modell winke-laufgeloste Photoemissionstomografie-Karten und vergleichen sie mit experimentellgemessenen Karten. Im dritten Kapitel untersuchen wir Dihydrotetraazapentaceneauf Cu(110)-(2x1)O. Wir bestimmen den optimalen Adsorptionsplatz, indem wirzuerst die Molekule auf verschiedenen Adsorptionsplatzen relaxieren und danach dieEnergien der verschiedenen Geometrien vergleichen. Des Weiteren berechnen wirdie Diffusionsbarriere zwischen zwei benachbarten optimalen Adsorptionsplatzen.Außerdem simulieren wir fur diese verschiedenen Geometrien RTM-Bilder in derTersoff-Hamann-Naherung und vergleichen das simulierte RTM-Bild der optimalenAdsorptionsgeometrie mit experimentell verfugbaren RTM-Daten.

v

vi

Acknowledgements

First of all I want to express my special gratitude to my supervisor Professor PeterPuschnig for his guidance and for patiently answering all of my questions. I wantto also thank Bernd Kollmann, Mathias Schwendt and Daniel Lueftner for helpfuldiscussions. I also thank my predecessor Jana Fuchsberger for helpfully answeringquestions regarding her thesis. Finally I want to offer my special thanks to friendsand family for support.

vii

viii

Contents

Abstract iii

Kurzzusammenfassung v

Acknowledgements vii

1 Introduction 1

2 Theory 32.1 Density Functional Theory . . . . . . . . . . . . . . . . . . . . . . . . 3

2.1.1 The electronic Hamiltonian and the density as the basic variable 32.1.2 The Kohn-Sham auxiliary system . . . . . . . . . . . . . . . . 52.1.3 Exchange and Correlation . . . . . . . . . . . . . . . . . . . . 7

2.2 DFT in practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8Plane Wave Expansion . . . . . . . . . . . . . . . . . . . . . . 9Simulation of surfaces . . . . . . . . . . . . . . . . . . . . . . 9Van-der-Waals Interactions . . . . . . . . . . . . . . . . . . . . 9Dipole Corrections . . . . . . . . . . . . . . . . . . . . . . . . 11

2.3 Workfunction and Workfunction Changes . . . . . . . . . . . . . . . . 122.4 Projected Density of States . . . . . . . . . . . . . . . . . . . . . . . 132.5 Photoemission Momentum Maps . . . . . . . . . . . . . . . . . . . . 142.6 Theory of Scanning Tunneling Microscopy . . . . . . . . . . . . . . . 15

3 Results 173.1 Tetracene on Ag(110) . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

3.1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183.1.2 The ”Huang Cell” . . . . . . . . . . . . . . . . . . . . . . . . . 20

Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20Density of States . . . . . . . . . . . . . . . . . . . . . . . . . 21Photoemission Momentum Maps . . . . . . . . . . . . . . . . 23Workfunction . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

3.1.3 Large and Small ”Diamond” . . . . . . . . . . . . . . . . . . . 24Geometries . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24Projected Density of States . . . . . . . . . . . . . . . . . . . 25Workfunctions . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

3.1.4 Cross . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29Projected Density of States . . . . . . . . . . . . . . . . . . . 29ARPES-maps . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

ix

Contents

Workfunction . . . . . . . . . . . . . . . . . . . . . . . . . . . 323.1.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

3.2 DHTAP on Cu(110)-(2x1)O . . . . . . . . . . . . . . . . . . . . . . . 343.2.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343.2.2 Adsorption Geometry . . . . . . . . . . . . . . . . . . . . . . . 36

DHTAP-chains . . . . . . . . . . . . . . . . . . . . . . . . . . 383.2.3 Potential energy surface . . . . . . . . . . . . . . . . . . . . . 383.2.4 Charge rearrangements and workfunction change. . . . . . . . 403.2.5 STM-images . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

Constant current STM images of the adsorption sites . . . . . 45Comparison with experiment . . . . . . . . . . . . . . . . . . . 45

3.2.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

Summary 49

Bibliography 51

Appendix A Computational Details 55A.1 Tetracene . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55A.2 DHTAP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

Appendix B Kohn-Sham Orbitals of Tetracene in the Gas Phase 59

x

Chapter 1

Introduction

The world in which we live in today would be unimaginable without semiconductorelectronics. Computer screens have a backlight made out of light emitting diodes,the mouse functions with a semiconductor laser, the keyboard uses a microcontrollerwith built in semiconductor circuits to tell the computer which key is pressed, thechip at the heart of the computer is made out of semiconductor transistors, on state-of-the-art computers files are saved on solid state drives, which again use semicon-ductor technology to save the bits and bytes. Looking at the smartphone one seesbasically all the same elements only miniaturized. The smartphone also likely has acamera: this camera captures light by means of a charge coupled device-chip, whichis again a semiconducting device.

To build this plethora of semiconducting electronics, various elements from the pe-riodic table including metals and half-metals are needed, e.g. Gallium, Arsenic,Indium, Tin, Germanium, etc. One of the most used materials for all these devicesis silicon. There is no shortage of silicon in sight: it is the second most abundantelement in the earth’s crust after oxygen [1]. However, the fabrication of siliconwith a grade of purity needed for semiconductor devices has an energetic and envi-ronmental cost: in 2002 the production of one square centimeter of a silicon waferconsumed 1.5 kWh of electrical energy which amounts to about 1.5 MJ of energycontained in fossil fuels [2].

It is therefore desirable to find an alternative to silicon based electronics. Oneroute is organic electronics which is rooted in organic i.e. carbon based moleculesand polymers. The goal of this research endeavor is to find organic materials withcomparable electrical properties as current semiconductor materials.

Organic electronics have already entered the electronics market: the displays ofnewer smartphones use the so-called AMOLED technology, a technology based onorganic light emitting diodes (OLEDs). The manufacturing process is also quitedifferent: organic materials can be printed using standard printing techniques. Thisallows for thin, flexible displays and solar panels, opening up a market previouslynot reached by silicon-based electronics. And while still not on the market today,research has lead to ever increasing efficiencies of organic photovoltaic cells.

The electronic performance and stability of organic molecules in the context ofsemiconductor devices is crucially determined by the organic/inorganic interface.

1

Chapter 1. Introduction

Consider as two examples an organic transistor and an organic light emitting diode:in the former one still needs a source and a drain, and in the latter one still needsa cathode and an anode. In both cases this role will necessarily be played bymetals.

Molecules, metals and their interface are quantum mechanical systems and wouldneed to be investigated by solving Schrodinger’s equation. Since the nuclei are muchheavier than the electrons one can as a first step simplify this problem a bit by onlyconcentrating on the electrons. However, solving this many-body problem for manyelectrons has shown to be not only computationally demanding, but also physicallyquestionable [3]. To facilitate the investigation of these systems density functionaltheory (DFT) has proven to be successful: instead of solving for the many-bodywavefunction of N electrons Ψ(~r1, . . . , ~rN), described by 3N variables, one choosesa description in terms of the electron density n(~r ), a function of 3 variables.

In this thesis we will investigate two different organic/metal interfaces by means ofDFT: tetracene on Ag(110) and dihydrotetraazapentacene on Cu(110)-(2x1)O. Wewill demonstrate how to use DFT in practice to determine electronic properties ofthe molecules on the surface and how to tell if the molecules are charged or not,how to determine workfunction changes induced by adsorption of the molecules onthe surface, how to determine the orientation of the molecules on the surface andhow to simulate and interpret scanning tunneling microscopy (STM) images.

In the first chapter we review the theory: we give a brief introduction into DFT andmention several topics which are pertinent to real world DFT calculations. We thenexplain theoretical concepts which surface often in this thesis: the workfunction andworkfunction changes, the projected density of states, photoemission momentummaps and finally the theory of the simulation of STM images. The next chaptershows the results of the calculations of the two interfaces. In the first section theresults of tetracene on Ag(110) are presented: for four different geometries we showand discuss the projected densities of states and the workfunctions. For two selectedgeometries we also show photoemission momentum maps and discuss them in thecontext of available experimental data. In the second section the results of thecalculations of Dihydrotetraazapentacene on Cu(110)-(2x1)O are presented. Wedetermine the optimal adsorption site and calculate the potential energy surfacebetween two adjacent optimal adsorption points. We then calculate the workfunctionchange and charge rearrangements upon adsorption of the molecule. Finally wesimulate STM images and compare them to experimentally available ones.

2

Chapter 2

Theory

In this chapter we review the necessary theoretical framework. First an overviewof DFT is given, afterwards the theoretical concepts used throughout the thesis areintroduced: the partial density of states, the simulation of angle-resolved photoe-mission maps and finally the theory of scanning tunneling microscopy.

Throughout the thesis atomic units are used. In this system of units

h = melectron =e2

4πε0≡ 1.

2.1 Density Functional Theory

In this section we review the basics of density functional theory. For fully-fledgedintroductions to density functional theory we refer the reader to Refs. [4, 5], and thelecture notes of Puschnig [6]. For a more extensive treatment of electronic structurecalculations we refer the reader to Ref. [7].

2.1.1 The electronic Hamiltonian and the density as the ba-sic variable

To describe the properties of atoms, molecules and solids one needs to solve thenon-relativistic time-independent Schrodinger equation

HΨ(~r1, . . . , ~rN) = EΨ(~r1, . . . , ~rN) (2.1)

with the Hamiltonian [6, 7]:

H = −1

2

∑i

∆i︸ ︷︷ ︸T

+1

2

∑i,j;i 6=j

1

|~ri − ~rj|︸ ︷︷ ︸Uee

+∑i

v(~ri)︸ ︷︷ ︸V

, (2.2)

where T is the kinetic energy operator, Uee the electron-electron interaction and Vis the interaction of the electrons with the electrostatic field of the fixed nuclei. This

3

Chapter 2. Theory

potential is customarily called the external potential v(~ri):

v(~ri) = −∑j

Zj

|~ri − ~Rj|. (2.3)

Solving the non-relativistic time-independent Schrodinger equation with the Hamil-ton operator 2.2 and the many-body wavefunction Ψ completely determines all prop-erties of the system at hand, in particular, it yields the ground state energy E andthe ground state electron density according to the following relation:

n(~r ) = N ·∫d3r2· · ·

∫d3rN |Ψ(~r, ~r2, . . . , ~rN)|2. (2.4)

The idea of density functional theory (DFT) is to replace the wavefunction at thecenter of description with the electron density n(~r ): instead of using a functionwhich depends on 3N variables we seek a description of the electronic structure interms of a function of only 3 variables.

First we need a description which is equivalent to the Schrodinger equation 2.1and where the dependency on the electron density is suggested. For this we turnto the Rayleigh-Ritz variational principle. [8, 9]. This principle states that anapproximate ground state eigenfunction Ψ can be found by extremizing the energyfunctional

E[Ψ] = 〈T 〉+ 〈Uee〉+

∫d3r v(~r )n(~r ) (2.5)

under the constraint 〈Ψ|Ψ〉 = 1:

δE = δ

(〈Ψ|H|Ψ〉〈Ψ|Ψ〉

)!

= 0. (2.6)

Then we see from eq. (2.4) that the density is a functional of the many-body wave-function Ψ, the wavefunction on the other hand is itself (from eq. (2.1)) a functionalof the external potential v(~r ). This means that the external potential determinesthe density:

v(~r )⇒ n(~r ).

The question arises whether this mapping between external potential and densityis unambiguous. i.e. if the statement is also true if we reverse the direction of thearrow. The affirmative answer is given by Hohenberg and Kohn [10]:

The external potential v(~r ) is a unique functional of the electron density n(~r ).

This in turn means that the electron density determines the Hamiltonian uniquely,since the ground state Hamiltonian itself depends on v(~r ). Since all ground-stateproperties are determined by the Hamiltonian, this finally means that all ground-state properties are uniquely determined by the electron density n(~r ).

4

Section 2.1. Density Functional Theory

Since the ground-state wavefunction Ψ is now determined by the density, the expec-tation values in eq. (2.5) are also functionals of the density. The energy functionalof eq. (2.5) can then be written as

E[n(~r )] = T [n(~r )] + Uee[n(~r )] +

∫d3r v(~r )n(~r ) (2.7)

≡ F [n(~r )] +

∫d3r v(~r )n(~r ), (2.8)

where we have defined the universal functional F [n(~r )] ≡ T [n(~r )]+Uee[n(~r )].

That the minimum of this energy functional E[n(~r )] gives the correct density wasalso proven by Hohenberg and Kohn [10]:

For any given external potential v(~r ) the global minimum of E[n(~r )] is the exactground state energy E0 and the density which minimizes E[n(~r )] is the exact

ground state density n0(~r ).

So far we have shown that a description using the density is possible, but we havenot shown how to actually calculate the density. Also, no precise meaning was givento F [n(~r )]. One approach which brings us closer to actual calculations was providedby Kohn and Sham one year after [10].

2.1.2 The Kohn-Sham auxiliary system

The idea of [11] is to introduce an auxiliary system of non-interacting electrons.Instead of a many-body wavefunction Ψ(~r1, . . . , ~rN) and the many-body Hamilto-nian 2.2 we then can use single particle wavefunctions ψ(~r ), called the Kohn-Shamorbitals, and can work with a single-particle Hamiltonian

H = −1

2∆ + vs(~r ), (2.9)

where vs(~r ) is the Kohn-Sham potential, which will be defined below. The den-sity is obtained by summing over the square moduli of all occupied Kohn-Shamorbitals:

n(~r ) =∑occ.

|ψi(~r )|2. (2.10)

In order to obtain the Kohn-Sham potential and thus the single particle orbitals weproceed as follows. First we write the kinetic energy Ts[n(~r )] in F [n(~r )] as a sumof single-particle energies

Ts[n(~r )] = −1

2

∑i

∫d3r |∇ψi(~r )|2. (2.11)

Then we split the electron-electron interaction into two parts: the Hartree energyUH [n(~r )] and the exchange-correlation functional Exc[n(~r )]:

Uee[n(~r )] ≡ UH [n(~r )]+Exc[n(~r )] with UH [n(~r )] =1

2

∫d3r

∫d3~r ′

n(~r )n(~r ′)

|~r − ~r ′|.

5

Chapter 2. Theory

(2.12)

The full expression of the universal functional is then

F [n(~r )] ≡ Ts[n(~r )] + UH [n(~r )] + Exc[n(~r )] (2.13)

= −1

2

∑i

∫d3r |∇ψi(~r )|2 +

1

2

∫d3r

∫d3~r ′

n(~r )n(~r ′)

|~r − ~r ′|+ Exc[n(~r )]. (2.14)

To proceed we turn to the Rayleigh-Ritz principle 2.6, which states that an approx-imate ground-state density is obtained by varying the energy functional E[n(~r )] =F [n(~r )] +

∫d3r v(~r)n(~r) with respect to the density and setting the variation zero.

Since the kinetic energy term depends on the orbitals explicitly we can also vary thewavefunctions and use the chain rule where necessary [7]. We can incorporate thenormalization condition 〈ψi|ψi〉 = 1 with an Lagrangian multiplier ε:

δE = δ

{F [n(~r )] +

∫d3r v(~r )n(~r )− εi

(∫|ψi(~r )|2 − 1

)}!

= 0. (2.15)

The individual terms give [7]:

δTs[n(~r )]

δψ∗i (~r )= −1

2∆ψi(~r )δψ∗i (~r ), (2.16)

δUH [n(~r )]

δψ∗i (~r )=

∫d3~r ′

n(~r ′)

|~r − ~r ′|δn(~r )

δψ∗i (~r ), (2.17)

δExc[n(~r )]

δψ∗i (~r )=δExc[n(~r )]

δn(~r )

δn(~r )

δψ∗i (~r ), (2.18)

δ(3rd term)

δψ∗i (~r )= v(~r )

δn(~r )

δψ∗i (~r ), (2.19)

δ(4th term)

δψ∗i (~r )= −εiψi(~r ). (2.20)

Adding everything together and using

δn(~r )

δψ∗i (~r )=

δ

δψ∗i (~r )

∑occ.

ψ∗j (~r )ψj(~r ) = ψi(~r ) (2.21)

we obtain{(−1

2∆ +

∫d3~r ′

n(~r ′)

|~r − ~r ′|+δExc[n(~r )]

δn(~r )+ v(~r )− εi

)ψi(~r )

}δψ∗i (~r )

!= 0. (2.22)

Since this equation must be fulfilled for any variation δψ∗i (~r ), the term in the curlybraces must vanish. We then finally get the Kohn-Sham equations(

−1

2∆ + vs(~r )

)ψi(~r ) = εiψi(~r ) (2.23)

6

Section 2.1. Density Functional Theory

with the Kohn-Sham potential

vs(~r ) =

∫d3~r ′

n(~r ′)

|~r − ~r ′|+δExc[n(~r )]

δn(~r )+ v(~r ) (2.24)

and the exchange-correlation potential

vxc(~r ) =δExc[n(~r )]

δn(~r ). (2.25)

The Kohn-Sham-equations, the Kohn-Sham-potential and the equation for the den-sity 2.10 need to be solved self-consistently: first we begin by assuming a startingdensity n0(~r ), with this density we calculate the Kohn-Sham potential vs,0(~r ). Withthis potential we can the solve the Kohn-Sham equations H(vs,0(~r ))ψ = εψ. Fromthis in turn we get a new density n1(~r ), we mix the old and new density and calculatethe new Kohn-Sham potential vs,1(~r ) and so on.

This completes the mapping from a many-body problem to a single-particle scheme.The many-body effects – exchange and correlation – are all encompassed in theexchange-correlation potential vxc(~r ).

2.1.3 Exchange and Correlation

Until now no approximations have been made, and if the exchange-correlation energyExc(~r ) were known exactly then the problem of electronic structure would be solvedcompletely, meaning that from the Kohn-Sham scheme we would get the exactground-state density and exact ground-state energy.

The difficulty of DFT lies in the fact that there is (yet) no exact expression ofExc(~r ), and the usefulness of any DFT calculation depends on the quality of theapproximation used for the exchange-correlation energy at hand.

Before we try to acquire some intuition for the exchange-correlation energy we wantto give precise meaning to the different terms: ”exchange” and ”correlation”. (Thediscussion in this paragraph closely follows [4].)

First we write the exchange-correlation energy as a sum of an exchange term Exand a correlation term Ec:

Exc[n(~r )] = Ex[n(~r )] + Ec[n(~r )]. (2.26)

Then we define Ex[n(~r )] as the difference between the electron-electron energy ofthe non-interacting system and the Hartree energy:

Ex[n(~r )] =⟨ψminn

∣∣Uee

∣∣ψminn

⟩− UH [n(~r )]. (2.27)

ψminn is the wavefunction of the non-interacting electron system which minimizes the

energy functional and which yields a given density n(~r ). Ec[n(~r )] on the other handis defined as

Ec[n(~r )] =⟨Ψminn

∣∣T + Uee

∣∣Ψminn

⟩−⟨ψminn

∣∣T + Uee

∣∣ψminn

⟩, (2.28)

7

Chapter 2. Theory

where Ψminn is the wavefunction of the full system of interacting electrons which

yields a given density n(~r ) and which minimizes 〈T + Uee〉.

Adding eq. (2.27) and eq. (2.28) and using the concept of coupling-constant inte-gration one can derive the expression [4]

Exc[n(~r )] =1

2

∫∫d3rd3~r ′

n(~r )nxc(~r, ~r′)

|~r − ~r ′|, (2.29)

where nxc(~r, ~r′) is the coupling constant averaged exchange-correlation hole:

nxc(~r, ~r) =

∫ 1

0

dλ nλxc(~r, ~r′). (2.30)

The exchange-correlation energy can therefore be interpreted as the electrostaticenergy between each electron and its surrounding exchange correlation hole. Thishole is created by three effects:

• the self interaction correction, since an electron cannot interact with itself,

• Pauli’s principle, which tends to keep electrons with equal spin apart,

• Coulomb repulsion, which keeps all electrons apart, regardless of their spin.

Now we turn to approximations of Exc[n(~r )]. The simplest one is the so-called localdensity approximation. In this approximation, the exchange-correlation energy is ateach point proportional to the local density of electrons and the exchange-correlationenergy density of a homogeneous electron gas with that density [7]:

ELDAxc [n(~r )] =

∫d3r n(~r )εhom.

xc (n(~r )). (2.31)

In thesis we employ the generalized gradient approximation-functional by Perdew,Burke and Ernzerhof [12]. In this approximation, the exchange-correlation energyis at each point proportional to the local density of electrons and to the exchange-correlation energy density. This time, also density gradients are included in theexpression for εhom.

xc (n(~r )) [7]:

EGGAxc [n(~r )] =

∫d3r n(~r )εhom.

xc (n(~r ), |∇n(~r )|, . . . ). (2.32)

2.2 DFT in practice

In the last section we reviewed the basic principles of DFT. In this section we discusssome aspects which need to be kept in mind when doing actual DFT calculations,specifically, when using the Vienna Ab-initio Simulation Package (VASP) [13, 14].For a good introduction into VASP we refer the reader to [15].

8

Section 2.2. DFT in practice

Plane Wave Expansion

One main characterizing feature of available DFT codes is the employed basis set.VASP uses plane waves

φ~k+ ~G(~r ) =1√Vei(

~k+ ~G)·~r (2.33)

as a basis, where ~G is a reciprocal lattice vector, ~k is a Bloch vector and V isthe crystal volume. Note that plane waves are orthonormal, complete and naturallysatisfy Bloch’s theorem. Expanding the Kohn-Sham orbitals ψn~k(~r ) with band index

n and Bloch vector ~k in plane waves gives

ψn~k(~r ) =1√Vei~k·~r

∞∑i=1

cn~k(~Gi )e

i ~Gi·~r. (2.34)

We note that the sum in eq. (2.34) is an infinite sum, however, in practice it isnot possible to use infinitely many basis functions. Therefore we need to truncatethe sum at some ~Gmax, which means that all basis functions having energy below acertain cut-off energy are included:

1

2|~k + ~G|2 < Ecut =

1

2~G2

max. (2.35)

In VASP this energy can be set with the ENCUT parameter. In all our calculationswe set the ENCUT parameter manually. In particular we took care that in calcula-tions where we compared the molecule/substrate, substrate-only and molecule-onlysystems the ENCUT parameters where the same in all three INCAR files, see also cms.

mpi.univie.ac.at/vasp/vasp/When_set_ENCUT_and_ENAUG_hand.html .

Simulation of surfaces

To simulate surfaces we used the repeated slab approach. In this approach the surface(several layers of substrate with adsorbed molecules) is in the x,y-plane and thedifferent surfaces are separated by a vacuum layer, as depicted in figure 2.1.

The convergence of the calculated properties depends on the thickness of this vacuumlayer as well as on the number of atomic layers in the surface slab [15].

Van-der-Waals Interactions

Van der Waals interactions, or so-called London dispersion forces, arise from instan-taneously induced dipoles at a given distance and are, for instance, responsible forthe (weak) intermolecular interactions between organic molecules or also contributeto the interaction of molecules with (metallic) surfaces. While an exact treatmentof correlation effects within the framework of DFT would naturally include vdWinteractions, the (semi)-local LDA and GGA approximations do not capture those

9

Chapter 2. Theory

x, y

z

Figure 2.1: Depiction of the repeated slab approach.

non-local correlations. In the past decade, a number of approaches have been de-veloped to deal with this problem in the DFT framework [16].

In this thesis, van-der-Waals (vdW) interactions are treated with the Tkatchenko-Scheffler method [17]1. To incorporate the vdW energy a term of the form

EVdW = −∑A,B

fdamp ·C6AB

(RAB)6 (2.36)

is added to the total energy computed from DFT, where the sum runs over all pairsof atoms, C6AB is the C6 coefficient and RAB the distance between atoms A andB. fdamp is a damping function, counteracting the divergence of the R6

AB at shortdistances.

fdamp is a function of the distances RAB and the vdW-radii R0i , C6AB on the other

hand is a function of the polarizabilities αi and the homonuclear dispersion coeffi-cients C6ii:

fdamp = fdamp(RAB, R0A, R

0B), (2.37)

C6AB = C6AB(α0A, α

0B, C

06AA, C

06BB). (2.38)

In these expressions the various parameters are defined for free atoms , e.g. thepolarizability α0

C is the polarizability of an carbon atom in the gas phase.

The idea of Tkatchenko-Sheffler is to use the free-atom values for αi, R0i and C0

6ii

together with the Hirshfeld partitioning νi (see link in footnote 1 for a definition ofν) to calculate effective polarizabilities, vdW-radii etc. for atoms in a molecule or

1Also cms.mpi.univie.ac.at/wiki/index.php/Tkatchenko-Scheffler_method

10

Section 2.2. DFT in practice

solid:

αeffi = νiα

0i , (2.39)

Ceff6ii = ν2

i C06ii, (2.40)

Reff0i = ν

1/3i R0

0i. (2.41)

In VASP calculations the Tkatchenko-Sheffler method is activated by including aline IVDW = 2 in the INCAR-file. The free-atom parameters are tabulated, here welist the parameters used in this thesis2:

Parameter INCAR-name C H N Cu O Ag

α0i VDW ALPHA 12 4.5 7.4 10.9 5.4 15.4C0

6ii VDW C6AU 46.6 6.50 24.2 59 15.6 122R0

0i VDW R0 1.9 1.64 1.77 1.27 1.69 1.35

In VASP the parameters are set by including appropriate arrays in the INCAR file,like this:

IVDW = 2VDW alpha = 15 .4 12 4 .5VDW C6AU = 122 46 .6 6 .5VDW R0 = 1.35 1 .9 1 .64

The order in which the parameters are given in the array must be the same as theorder of atoms in the POSCAR-file. In the example above the order is Ag - C - H.

Dipole Corrections

The adsorption of molecules on surfaces generally alters the workfunction (see nextsection), meaning that the electrostatic potential above the substrate/molecule sidediffers from the electrostatic potential above the bare surface.

However, since we employ the repeated slab approach with periodic boundary con-ditions, the electrostatic potentials on either side of the slab have to be equal at thecell boundary. This continuous change in the electrostatic potential induces via therelation ~E = −~∇φ a spurious electric field. One remedy would be to increase thethickness of the vacuum layer which would reduce the magnitude of this spuriouselectric field. However, this would lower the computational efficiency since a largerunit cell leads to an increased number of basis functions when keeping the planewave cut-off constant.

To overcome this, Neugebauer and Scheffler [18] introduced the concept of addingan artificial dipole which counteracts the spurious electric field originating from thedifferent electrostatic potentials. This artificial dipole is clearly visible in all plotsof the plane averaged electrostatic field, see e.g. fig. 3.8, page 24: at z ∼ 25 A wesee a step, this is where the artificial dipole is placed. The size of this step indicates

2VDW C6AU is the VDW C6 = C06ii parameter in atomic untis

11

Chapter 2. Theory

the workfunction change and is determined self-consistently during a DFT groundstate calculation.

In VASP this dipole correction is enabled by switching on the LDIPOL parameter inthe INCAR file:

LDIPOL = .TRUE.

In our calculations the surface is parallel to the x, y-plane, while the vacuum regionextends into the z-direction. In this case we need to enable the dipole correctionparallel to the z-direction:

IDIPOL = 3

2.3 Workfunction and Workfunction Changes

The workfunction is defined as the energy needed to remove an electron from theFermi-level into the vacuum:

Φ = Evac − EF. (2.42)

On bare metal surfaces, the work function is primarily influenced by the surfacedipole layer: electrons spill from the metal surface into the adjacent vacuum, causinga local depletion of electrons in the metal near the surface and an accumulation ofelectrons in the adjacent vacuum. These two local charge rearrangements ∆φ =ρ give rise to a dipole layer at the surface of a metal and in turn to an electricfield.

The electric field caused by this depletion is called the surface dipole and it counter-acts the electron flow into the vacuum until equilibrium is reached. The workfunctionis then increased by the work needed to move an electron from the metal throughthis surface dipole into the vacuum:

∆Φ =

∫ vacuum

metal

~Edipole(~r ) · d~r. (2.43)

Adsorption of molecules on the metal surface change the workfunctions due to twoeffects:

The Pauli push-back effect: Due to Pauli’s principle, the electrons of the moleculepush spilled electrons back into the surface. This decreases the surface dipoleand decreases the workfunction.

Charge transfer: Charge transfer from the surface to the molecule increases thesurface dipole and therefore increases the workfunction.

The workfunction and workfunction changes can be calculated from VASP by ana-lyzing the electrostatic potential which is stored in the LOCPOT file. More precisely,in this thesis we calculate the plane-averaged local potential

φ(z) =1

NxNy

Nx∑i=1

Ny∑j=1

φ(xi, yj, z), (2.44)

12

Section 2.4. Projected Density of States

where Nx and Ny are the number of grid-points in the x and y direction and φ isthe local potential as it is recorded in the LOCPOT file.

The workfunction above a surface (either bare substrate or with adsorbed molecules)is then the difference between the plane-averaged local potential in the vacuum abovethe respective surface and the Fermi energy EF :

Φ = φ(vacuum)− EF (2.45)

EF can be extracted from various VASP files, e.g. the DOSCAR file.

The workfunction change upon adsorption of molecules can then be calculatedby

∆Φ = Φsurface+molecules − Φbare surface. (2.46)

2.4 Projected Density of States

Another quantity we will frequently calculate in this thesis is the projected densityof states. First we define the density of states ρ(E) [7]:

ρ(E) =1

Nk

∑i

BZ∑~k

δ(εi,~k − E), (2.47)

where Nk is the number of k-points in the Brillouin-zone and εi,~k is the energy of the

energy band number i at the Brillouin-zone point ~k. The sum runs over all bandsand ~k-points in the Brillouin zone. ρ(E)dE is the number of states between E andE + dE per unit cell.

Inserting a complete set of Kohn-Sham orbitals 1 =∑|ψj〉 〈ψj|, multiplying from

the left with an atomic orbital 〈φ| (e.g. an s-orbital) and from the right with |φ〉and using the orthonormality 〈φ|φ〉 = 1 gives

ρφ(E) =1

Nk

B.Z.∑i,~k

∑j

| 〈φ|ψj〉 |2δ(εi,~k − E), (2.48)

where the second sum runs over all Kohn-Sham orbitals. The subscript φ is notationand indicates that we projected the density of states on orbital φ.

ρφ(E) is the contribution of orbital φ at energy E and B.Z.-point ~k to the totaldensity of states ρ(E), this projection of the total density of states on orbital φ iscalled projected density of states (pDOS).

In VASP this projection is enabled by setting the LORBIT parameter in the INCAR

file. Then, in the DOSCAR file a site-projected DOS is written, see https://cms.

mpi.univie.ac.at/wiki/index.php/DOSCAR. Site projected means that for eachion eq. (2.48) is calculated, where the different atomic orbitals φi are in the caseof LORBIT=11 an s-orbital, a px-orbital, a py-orbital etc, see the VASP documenta-tion.

13

Chapter 2. Theory

x

y

z

hω

kf||

kf⊥

~kf

e−

kf,x

kf,yαθ

φ

Figure 2.2: Schematic illustration of an angle-resolved photo-emission experiment.

To obtain the contribution of a molecule to the total density of states one needs tosum over all orbitals (s, px, py, . . . ) and over all ions of the respective molecule.

The pDOS contains information about the electronic structure of the molecule ad-sorbed on the surface. It shows the energetic alignment of the molecular orbitalsrelative to the Fermi energy. From this, the energy gap between the frontier orbitals,the highest molecular orbital (HOMO) and the lowest unoccupied molecular orbital(LUMO), can be inferred. Thereby, the pDOS also helps to clarify whether thereis charge transfer into the molecule: if the LUMO crosses the Fermi energy thencharge transfer took place. This is because the Fermi energy indicates the energy ofthe highest occupied state by an electron, when this energy is in the energy range ofthe lowest unoccupied molecular orbital this necessarily means that electronic statesof the previously unoccupied orbital are now occupied.

2.5 Photoemission Momentum Maps

Photoemission spectroscopy is based on the photoelectric effect which has been firstexplained by Einstein [19]: a photon with energy hω impinging on a metal surfaceejects a photoelectron from the metal surface. By conservation of energy, the kineticenergy of the electron is

Ekin = hω − Ebinding = hω − (Φ + Ei), (2.49)

where Φ is the metal’s workfunction and Ei is the energy of the photoelectron’sinitial state. Thus, in photoemission spectroscopy monochromatic light is used tokick out electrons from the surface, which will be analyzed in terms of their kineticenergy. If one uses UV light then information about the density of states at thesurface can be gained.

A step further in the description of the electronic structure using the photoelectric ef-fect can be achieved by a technique called angle-resolved photoemission spectroscopy(ARPES) [20]. As illustrated in Fig. 2.2, the incident photon impinging at an angleα with the surface normal z leads to the emission of a photoelectron with kineticenergy Ekin in direction (φ, θ).

14

Section 2.6. Theory of Scanning Tunneling Microscopy

Figure 2.3: Idea of the Tersoff-Hamann approximation. The probe tip is a distanced above the metal surface (hatched) at position ~r0. R is the radius of the potentialwell.

In this thesis we simulate so called ARPES momentum maps, which are maps ofthe photoemission intensity at a constant binding energy recorded over the full halfspace above the surface. Note that the parallel momentum components kx and kyare given by kx = k sin θ cosφ and ky = k sin θ cosφ, respectively, where k is the

magnitude of the emitted electron’s wave vector, thus Ekin = k2

2. Within the one-

step model of photoemission, the photoemission current is given by a Fermi’s goldenrule type expression [20]

I(Ekin;φ, θ) ∝∑i

∣∣∣〈Ψf (Ekin;φ, θ)| ~A · ~p |ψi〉∣∣∣2 δ(Ei + Φ + Ekin − hω). (2.50)

Here Ψf is the final state of the photoelectron, ~A is the polarization vector of theincident photon and ~p the momentum operator of the photoelectron. The sumruns over all occupied Kohn-Sham orbitals ψi. The delta function ensures energyconservation.

If we assume the final state to be a plane wave we obtain the following expressionfor the photoemission current [21, 22]

I(Ekin; kx, ky) ∝ | ~A · ~k|2∑i

∣∣∣〈ei~k·~r|ψi〉∣∣∣2 δ(Ei + Φ + Ekin − hω). (2.51)

Note that the photoemission current is now proportional to the Fourier transform ofall occupied initial states ψi times the polarization factor | ~A · ~k|2. This approxima-tion has been shown to lead to satisfying results for many metal/organic interfaces[23].

2.6 Theory of Scanning Tunneling Microscopy

Scanning tunneling microscopy (STM) is a technique developed by Gerd Binnigand Heinrich Rohrer in 1981 for which they received the Nobel Prize in Physics

15

Chapter 2. Theory

Figure 2.4: Bandstructure of the tunneling process, with positive (negative) biasvoltage applied to the surface on the left (right) part of the image. The hatchedregions indicate occupied states. When a negative voltage is applied, the electronsgain electrostatic energy, which raises their energy relative to the Fermi energy. Thisinduces a current from the tip into unoccupied states of the surface, in our case theLUMO. Applying a positive voltage lowers their energy relative the Fermi level bythe electrostatic energy. This induces a current from already occupied states of thesurface, in our case the HOMO, into the metal tip. Adapted from [24].

in 1986. STM enables microscopy of surfaces with atomic resolution. It is basedon electrons tunneling through the vacuum gap between the surface to be examinedand a conducting tip, which is brought very near to the surface to be examined. Theresulting tunneling current is a function of tip position, applied voltage, and the localdensity of states (LDOS) of the sample. Figure 2.4 visualizes the bandstructure ofthe tunneling process and clarifies the meaning of the positive and negative biasvoltages.

In this thesis we simulate STM images using the Tersoff-Hamann approximation[25]. In this approximation, the tip is modeled as a spherical potential well, and thewavefunction of the tip is assumed to be an s-state. The current is then [26]:

I ∝∑ν

|ψν(~r0)|2δ(Eν − EF ) = ρ(~r0, EF ), (2.52)

where ψν(~r0) are the wavefunctions of the surface evaluated at the center of theprobe tip, see fig. 2.3, and the sum runs over all wavefunctions of the surface. Notethat in this approximation, the current is proportional to the local density of statesof the surface.

It must be emphasized that the contrast observed in STM images does not neces-sarily reflect the true geometry of adsorbed molecules or of surfaces. Hence, theinterpretation of experimental STM images often requires insight from electronicstructure calculations, specifically, simulations of the local density of states. A par-ticular example of this interplay between experiment and theory will be shown inthe results of this thesis: section 3.2.5, page 45. Here, the local density of states– and hence the STM-image – of the molecule appears curved while the geometricstructure of the molecule is actually straight.

16

Chapter 3

Results

In this chapter we present the results of the performed calculations. Section 3.1contains the results of tetracene on Ag(110), section 3.2 the results of DHTAP onCu(110)-(2x1)O. Each section starts with an motivation, after which the results ofthe calculations are presented. Each section then ends with a conclusion.

17

Chapter 3. Results

Figure 3.1: Tetracene

3.1 Tetracene on Ag(110)

3.1.1 Motivation

Tetracene (fig. 3.1) is an organic semiconductor with promising applications as anactive layer in organic field-effect transistors [27, 28] and in organic light emit-ting field effect transistors [29, 30]. The interesting electro-optical properties of thetetracene molecule (C18H12), as depicted in Fig. 3.1, arise from its π-conjugatedelectron system. In particular the frontier orbitals, i.e., the HOMO and LUMOorbitals, are π-orbitals with an electron distribution which is delocalized over theentire molecule.

For the application in organic semiconducting devices, the molecule/substrate in-teraction plays a crucial role, since this interface determines charge rearrangementsbetween surface and molecule and thereby governs the work function [31, 32]. Theelectronic structure of the interface is very sensitive to the precise geometric ar-rangement of the very first layer of molecules. It is therefore important to know theorientation of the molecule on the substrate.

In a previous study [33] the tetracene/Ag(110) interface has already been investi-gated by means of density functional calculations: two different monolayer structureshave been considered, one where the long axis of tetracene is oriented parallel tothe close-packed Ag-rows, and another structure where the molecules are alignedperpendicular to the row direction.

In particular, simulated photoemission tomography maps have been compared totheir experimental counterparts. This is depicted in fig. 3.2 and fig. 3.3. In theexperimental energy distribution curve (EDC), one observes four emissions whichcould be assigned to tetracene, which are denoted as M1, M2, M3 and M4. Thecomparison with the calculated projected density of states (pDOS) for monolayers oftetracene suggests that M1 can be associated with the lowest unoccupied moleculeorbital (L), which gets partially filled due to the interaction with the substrate, whileM2, M3 and M4 could tentatively be assigned to the highest occupied molecularorbital H, H-1 and H-2, respectively.

While the assignment M1=L has been confirmed by the photoemission angular dis-tribution maps (or momentum maps) reproduced in fig. 3.3 and thereby also helpedto clarify the molecular orientation, the situation for the lower lying molecular fea-tures is less clear. In particular, the origin of M2 and M3 separated by 0.9 eV, bothappearing to have the photoemission distributions of the highest occupied molecularorbital (H), emerged as an open problem.

18

Section 3.1. Tetracene on Ag(110)

Figure 3.2: Projected density of states of tetracene oriented parallel (orange orgray in grayscale print) and perpendicular (blue or black in grayscale print) to theAg-rows. Green: experimental electron distribution curve. Reproduced from [33].

Figure 3.3: Photoemission tomography maps of tetracene oriented parallel to theAg-rows. Top: Simulated photoemission maps. Bottom: Experimental photoemis-sion maps. The interpretation of the difference between a theoretical and an exper-imental photoemission maps (H-1 and M3, respectively) remains an open problem.Reproduced from [33].

19

Chapter 3. Results

One proposed solution suggests that the unit cell contains two molecules, where thetwo molecules occupy different adsorption sites. This may give rise to an energeticsplitting of the electronic states, in particular, of the HOMO.

In this chapter, we investigate this proposition further by determining the projecteddensity of states and the simulated ARPES-maps of four different adsorption geome-tries with two molecules per unit cell and by comparing them to the experimentalfindings. In what follows each of the four different geometries is presented in a sep-arate section. Each section contains the respective theoretical results comprised ofthe respective adsorption sites, projected density of states, workfunction variationsand photoemission momentum maps.

3.1.2 The ”Huang Cell”

Geometry

As mentioned above, in the previous study it has been concluded that tetraceneadsorbs parallel to the closed packed rows of Ag(110) [33]. For the DFT calculations,the following epitaxial matrix has been considered

A =

(6 00 3

), (3.1)

with one molecule per unit cell. The coverage is then 0.46 molecules/nm2.

On the other hand, the experimental study by Huang et al. [34] has found thatat a somewhat higher coverage of 0.64 molecules/nm2 tetracene forms an overlayerstructure described by the epitaxial matrix

AH =

(6 22 5

), (3.2)

with two molecules per cell. Note however, that in this cell both molecules areoriented perpendicular to the Ag-rows. Despite the fact that this disagrees with thefindings of Fuchsberger et al. [33], the structure proposed by Huang et al. appearsto be promising because a line profile curve suggests that the two molecules in theunit cell are not at the same height above the surface. This in turn may lead to anenergetic splitting the molecular states.

We investigated this claim by first setting up a structure with the epitaxial matrixsuggested by Huang et al., fig. 3.4, and then relaxing the molecules locally. Forall calculations concerning the ”huang cell” we used 5 layers of silver. In a secondstep, we froze in the geometry of molecule A at an adsorption height of 2.52 Awhile increasing the height of molecule B relative to the surface in 0.1 A increments,starting from a height equal to molecule A. The results of the calculations arepresented in fig. 3.5.

The energy minimum is found for a configuration in which the height of molecule Bis increased by 0.3 A, which clearly indicates that an adsorption structure with alter-nating molecule adsorption heights is energetically favorable. Note that our resultdiffers slightly from the result obtained by Huang et al., who found the energetic

20

Section 3.1. Tetracene on Ag(110)

A B [110]

[001]

Figure 3.4: The cell suggested by Huang et al. One of the molecules (in red, in thetext referred to as ”molecule A”) remains fixed in position while the height of thesecond molecule in the cell (in blue, in the text referred to as ”molecule B”) relativeto the surface is varied .

minimum at a height difference of 0.45 A. This may be attributed to differences inthe computational details of the used DFT calculations, for instance, the type ofvan-der-Waals correction scheme.

In the remainder of this section all calculations are performed with a cell in whichthe height of molecule B was increased by 0.3 A, corresponding to the total energyminimum.

Density of States

In view of the unclear interpretation of the experimental M2 and M3 emissionsmentioned above, we investigate whether a hint for a possible explanation of M2 andM3 can be provided by an energetic splitting of the HOMOs of the two inequivalentmolecules A and B.

To this end, the pDOS of the Huang cell is presented in fig. 3.6, where the solid anddashed lines correspond to molecule A and B, respectively.

The LUMOs of both molecules cross the Fermi edge, which indicates a partial fillingof the LUMOs and therefore charge transfer from the surface to both molecules.One also sees that the LUMO of molecule A, which is closer to the surface, isshifted towards higher binding energies, indicating a stronger charge transfer fromthe surface to molecule A. Conversely, the LUMO of molecule B is only slightlyoccupied which is to be expected since molecule B is further away from the surfaceand therefore interacting weaker with the silver substrate.

21

Chapter 3. Results

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

F-F

m��

/ e

V

�z / Å

Figure 3.5: Change in the total energy relative to the energy minimum F−Fmin asa function of the height increment ∆z added to the B molecules in fig. 3.4. Herethe energy minimum is found for a height increment of 0.3 A.

LL

HH

H−1H−2

Figure 3.6: pDOS of the Huang cell with two molecules per cell. Solid line: pDOSof molecule A. Dashed line: pDOS of molecule B with increased height. L: Lowestunoccupied molecular orbital. H: Highest occupied molecular orbital. The threedashed lines highlight at which energies (relative to the Fermi energy) the threephotoemission maps of fig. 3.7 were performed. The energies are (from right toleft): −1.38 eV,−2.55 eV and −2.70 eV.

22

Section 3.1. Tetracene on Ag(110)

(a) −2.7 eV (H−2) (b) −2.55 eV (H−1) (c) −1.38 eV (H)

(d) HOMO-2 (e) HOMO-1 (f) HOMO

Figure 3.7: Top row: Photoemission maps of the Huang cell. The caption for eachsub-figure indicates at which energy in the pDOS (fig. 3.6) the maps were simulated.These three energies are highlighted in fig. 3.6 by three dashed lines. Bottom row:Simulated ARPES-maps for tetracene in the gas phase. The label below each figureindicates which Kohn-Sham orbital was used in the simulation of the respectiveARPES-map.

Most importantly, however, no significant splitting of the highest occupied molecularorbitals of the two molecules is apparent.

Photoemission Momentum Maps

In this subsection, we present photoemission maps calculated from the Kohn-Shamorbitals of the tetracene/Ag(110) interface and a damped plane wave as a final statefor three selected binding energies.

We also show simulated photoemission maps for tetracene in the gas phase in figure3.7d, 3.7e and 3.7f. The ARPES-maps show, from right to left, the HOMO, HOMO-1 and HOMO-2. Comparing the maps of the tetracene/Ag(110) interface with thesethree maps confirms the assignment of figure 3.7a,3.7b and 3.7c : the form andthe extent in momentum space of all three maps of the interface are in very goodagreement with the gas-phase maps.

Comparison of the momentum maps shown in fig. 3.7 with the experimental mapsalso partly confirms the assignment of peaks indicated in the pDOS shown in fig. 3.6:the extent in momentum space and the form of the lobes of the emissions at −2.7 eVand −1.38 eV are similar to those of the experimental maps M4 and M2, respectively.The theoretical map at −2.55 eV on the other hand looks like the theoretical map ofthe HOMO-1 in fig. 3.7 and does not resemble the experimental map M3 of fig. 3.3e,page 19.

23

Chapter 3. Results

Figure 3.8: Workfunctions of the substrate Φsub, of the surface with adsorbedmolecules Φmol and the workfunction change ∆Φ = Φmol − Φsurf , all quantitiesin eVs and relative to the Fermi energy. The positions of the five layers of silver andalso of the molecules are indicated by arrows.

Workfunction

In figure 3.8 we present the workfunction change upon adsorption of tetracene onAg(110). The workfunction is lowered by −0.42 eV, which, according to the dis-cussion in section 2.3, indicates that effectively the workfunction decrease causedby the push-back effect dominates over the workfunction increase due to chargetransfer.

3.1.3 Large and Small ”Diamond”

Geometries

While the previous section has indicated that the presence of two inequivalentmolecules per unit cell could potentially explain the experimental findings, the re-sults differ with the experimental findings in two important aspects. First, themolecules are aligned perpendicular to the Ag-rows in the ”Huang-cell” while exper-iment indicates a parallel alignment, and second, the size of the calculated splittingturned out to be much smaller than the experimental value [33].

Therefore, we also tried two configurations with slanted cells, similar to the Huangcell, but with the molecules parallel to the closed-packed rows of Ag which aredepicted in 3.9. Note that both cells contain again two molecules and each moleculeis placed at a ”hollow”-site, which was found to be the energetically favourable bythe study cited earlier [33].

The configuration on the left (”diamond small”) is described by the epitaxial ma-trix (

5 11 4

), (3.3)

24

Section 3.1. Tetracene on Ag(110)

[110]

[001]

(a) ”small diamond”

[110]

[001]

(b) ”large diamond”

Figure 3.9: The supercells of the configurations considered in this section. Thesupercell of each configuration is highlighted by a black line. Each supercell containstwo molecules, in the figure the first molecule of each supercell is colored in red whilethe second molecule is colored in blue.

corresponding to a coverage of 0.87 molecules/nm2. The configuration on the right(”diamond big”) is described by the matrix(

6 11 4

), (3.4)

decreasing the coverage to 0.72 molecules/nm2.

We investigated if for these two configurations an alternating molecule height is alsoenergetically favorable. For this we proceeded as in the ”huang cell” section: we re-laxed both molecules locally, fixed molecule A of both configurations and increasedthe height of the B-molecules above the surface by 0.1 A increments. In all calcu-lations concerning the ”diamond” geometries we used 3 layers of silver. The resultsare presented in the fig. 3.10.

In both cases the energy minimum is found for a configuration in which bothmolecules have the same height above the surface. Since in both ”diamond” struc-tures the molecules are adsorbed at identical adsorption points we observe no sym-metry breaking, which is also reflected in the projected densities of states presentedbelow in fig. 3.11.

Projected Density of States

In contrast to the projected densities of states of the previous section, the pDOSof molecules A and B in the two diamond structures depicted in figure fig. 3.11 areidentical, owing to the fact that both molecules are adsorbed at the same heightand occupy identical adsorption sites. Next we see that the LUMOs of both con-figurations are occupied, indicating charge transfer to both molecules. However, no

25

Chapter 3. Results

Figure 3.10: Total energy changes versus height increment ∆z added to moleculeB (the blue molecules in fig. 3.9). F−Fmin is the increase in energy relative to theenergy minimum. Dashed line: Results of the ”small diamond” geometry. Solidline: Results for the ”large diamond” geometry. In both cases we see that theenergy minimum is attained for a geometry where both molecules have the sameheight above the surface.

explanation for the experimental HOMO emission patterns at two distinct bindingenergies can be deduced from these calculations.

Workfunctions

In figure 3.12 we present the workfunction change upon adsorption of tetracenein the two different ”diamond” geometries on silver. The workfunction is loweredin both cases by ∼ −0.56 eV, which, according to section 2.3, indicates that alsohere the workfunction decrease caused by the push-back effect dominates over theworkfunction increase due to charge transfer.

Here we note that the workfunction variation is the same, in spite of the fact the bothgeometries have different coverages: 0.87 molecules/nm2 and 0.72 molecules/nm2 forthe ”small” and ”large” diamond geometry, respectively. We suggest here that whilea higher coverage increases the charge transfer to the molecule, it also increasesthe push-back effect to the same degree. Both effects effectively cancel each otherout.

26

Section 3.1. Tetracene on Ag(110)

(a) ”diamond small”.

(b) ”diamond large”.

Figure 3.11: Projected densities of states of the two different ”diamond” geometries.In both cases the pDOS of both molecules are identical, since both molecules areat the same height above the surface and occupy identical adsorption sites. In bothcases the LUMO crosses the Fermi edge and is therefore occupied, indicating in bothcases charge transfer from the surface to the molecule.

27

Chapter 3. Results

(a) Averaged local potential of the ”small diamond” geometry.

(b) Averaged local potential of the ”large diamond” geometry.

Figure 3.12: Averaged local potential and workfunctions of the substrates withoutmolecule Φsub, of the surface with adsorbed molecules Φmol and the workfunctionchange ∆Φ = Φsub − Φsurf (all quantities in eVs and relative to the Fermi energy).The positions of the three layers of silver and also of the molecules are indicated byarrows.

28

Section 3.1. Tetracene on Ag(110)

Figure 3.13: STM image (37 nm× 37 nm) of the Ag(110) surface after deposition ofhalf a monolayer of tetracene, taken from [35].

3.1.4 Cross

Geometry

Finally, we consider a monolayer phase of tetracene/Ag(110) which has been foundby Takasugi et al. [35] at a coverage of 0.5 monolayer where STM images suggestthat tetracene forms cross shaped clusters (see fig. 3.13).

To investigate this structure we set up a supercell with an epitaxial matrix

A =

(6 00 5

)(3.5)

and two molecules per cell, where the second molecule is rotated by 90◦ with respectto the first and arranged such that the molecules form a cross if the unit cell isrepeated in both directions. Such an arrangement corresponds to a coverage of0.55 molecules/nm2. For the calculations in this section we used 3 layers of silver.The molecules parallel to the closed packed rows were put on the ”top” adsorptionsite, the molecules perpendicular to the closed packed rows were put on the ”hollow”adsorption site.

For this structure we also performed an ionic relaxation with VASP. Figure 3.14shows the ”cross” configuration after relaxation.

Projected Density of States

The projected density of states of the two molecules is shown in figure 3.15. Thefirst thing to notice is, that none of the LUMOs cross the Fermi edge, therefore thereis no charge transfer between the surface and the two molecules. Next thing to noteis that the orbital energies of the molecules lying perpendicular to the [110]-rowsare shifted towards higher binding energies.

29

Chapter 3. Results

[110][001]

Figure 3.14: The ”cross” configuration investigated in this section.

L‖

L⊥H‖

H⊥

H−1‖

H−2⊥

Figure 3.15: pDOS of the ”Cross” cell with two molecules per cell. Solid line:pDOS of the molecule parallel to the Ag-rows. Dashed line: pDOS of the moleculeperpendicular to the Ag-rows. L: Lowest unoccupied molecular orbital. H: Highestoccupied molecular orbital.

30

Section 3.1. Tetracene on Ag(110)

(a) −2.63 eV (b) −1.35 eV (c) 0.16 eV

(d) −2.48 eV (e) −1.26 eV (f) 0.26 eV

Figure 3.16: Simulated ARPES-maps for the ”Cross” configuration. The caption ofeach map indicates at which energy in fig. 3.15 the maps were simulated.

At first sight this may seem counter intuitive: the molecules parallel and on topof the [110]-rows seem to have more contact and therefore more interaction withthe surface, while the molecules perpendicular to the surface only cross the rows.This apparent contradiction can be explained inspecting the table B.1 of simulatedorbitals of tetracene on page 60. Looking at the HOMO and the HOMO-1 in realspace, we see that the orbitals have a node along the long axis of the molecule andthat the orbitals are centered at the carbon atoms, extending towards the hydrogenatoms. In the adsorption configuration considered here, the orbitals of the parallelmolecules are therefore largely located in trenches between the [110]-rows. Thereforethe tetracene orbitals of the molecules parallel to the rows do not have as muchoverlap with the orbitals of the surface, and as a consequence, cannot interact aseffectively as expected with the surface.

ARPES-maps

We show the simulated ARPES-maps in fig. 3.16. Comparing them with the ex-perimental maps in fig. 3.3, page 19, we first see a resemblance between the maps(b) and (e) and the map M2: both experimental and theoretical maps have lobes at

around 1 A−1

in the kx as well as in the ky-direction.

On the other hand the maps of the LUMOs, (c) and (f), are different from theexperimental counterpart, M1: the experimental map shows only two lobes in thekx direction, while the theoretical maps both show two lobes in the kx as well as in theky-direction. Also, the theoretical maps of the H-1 orbitals, (a) and (d), are differentof the experimental counterpart M3. We conclude that the ”cross” geometry is nota good candidate to explain the HOMO-like photoemission distribution M3.

31

Chapter 3. Results

Figure 3.17: Averaged local potential and workfunctions of the substrate Φsub, ofthe surface with adsorbed molecules Φmol and the workfunction change ∆Φ = Φsub−Φsurf (all quantities in eVs and relative to the Fermi energy). The positions of thethree layers of silver and also of the molecules are indicated by arrows.

Workfunction

We show the averaged local potential in fig. 3.17. The change in the workfunction is−0.45 eV, here again the push-back effect dominates over the charge transfer effect,just as in the previous three calculations.

3.1.5 Conclusion

The goal of this section was to find an explanation for a discrepancy between atheoretically predicted and an experimentally measured photoemission of tetraceneon Ag(110), where the photoemission map of the HOMO appears twice at differentbinding energies. In this work, we interpret this by assuming supercells with twomolecules at two different adsorption sites, causing an energetic splitting of theHOMOs.

Extending and building upon the work performed in [33] we have tried four newadsorption geometries: the ”Huang” cell, ”small diamond” and ”large diamond”and ”cross”. For each adsorption geometry we calculated the pDOS and - if anenergetic splitting was apparent in the pDOS - the ARPES-maps.

While for the ”diamond” configurations no energetic splitting was apparent in thepDOS, an energetic splitting could indeed be observed for the ”huang” and ”cross”configurations. However, the size of the splitting turned out to be too small toallow for a convincing explanation of the experimentally observed similarity of thephotoemission patterns M2 and M3. While in this thesis we could add new data tothe discussion the problem still remains open.

In addition, we calculated the change in workfunction for all four geometries. Allfour geometries show a decrease in workfunction of the order of −0.5 eV, indicatingthat in general the push-back effect dominates for these geometries.

32

Section 3.1. Tetracene on Ag(110)

Here we list the respective workfunction changes and coverages for future refer-ence:

Geometry coverage (molecules/nm2) ∆Φ(eV)

Huang Cell 0.64 −0.43small diamond 0.87 −0.56large diamond 0.72 −0.56

cross 0.55 −0.45

33

Chapter 3. Results

(a) PentaceneN

H

N

NN

H

(b) DHTAP

Figure 3.18: DHTAP (on the right) is a derivative of pentacene (on the left).

3.2 DHTAP on Cu(110)-(2x1)O

3.2.1 Motivation

Dihydrotetraazapentacene (C18H12N4, fig. 3.18b), in the following abbreviated asDHTAP, is a derivative of pentacene. Pentacene is a well researched molecule,interesting for its application in organic electronics [29, 36]. However, pentacenethin films are comparably instable towards photo-oxidation and also exhibit a lowsolubility [37]. This behavior can be traced back to the presence of only weakintermolecular interactions. One route to solve this problem is introduce polarchemical groups into the molecule which strengthen intermolecular interactions bythe hydrogen-bonds and thereby leads to more stable molecular films.

Introducing N atoms to the pentacene backbone leads to N-heteropentacenes. Inrecent years, N-heteropentacenes and their derivatives have arisen as a new familyof organic semiconductors with high performance in organic thin-film transistors[38]. Dihydrotetraazapentacene (DHTAP) is a particularly interesting derivative ofpentacene. It differs from pentacene by replacing the second benzene ring fromone end with a dihydropyrazine unit and by replacing the second ring from theother end with a pyrazine unit. The dihydropyrazine unit adds two electrons to thesystem, thereby stabilizing the molecule [39]. This is revealed in electronic structurecalculations by a lowering of its electron affinity and a raise in its ionization potential[40]. Secondly, the H-donor (N-H) and acceptor (N) sites lead to a strong molecule-molecule interaction which facilitates the formation of highly ordered structures[41, 42].

In this section, we study the geometric and electronic structure of monolayers ofDHTAP. DHTAP on Cu(110) has already been investigated in a previous study [43].Here, we investigate DHTAP on the Cu(110)-(2x1)O substrate, which is an oxygen-reconstructed Cu(110) surface, characterized by a missing-row structure comprisedof oxygen atoms in [110]-direction, where the distance between each oxygen row is√

2aCu ≈ 5.1 A. Thus, it is also a highly corrugated surface with deep trenchesbetween the oxygen rows as can be seen from fig. 3.19.

Our investigations are motivated by experimental scanning-tunneling microscopy(STM) images provided by P. Zeppenfeld and C. Becker [44]. Fig. 3.20 shows atypical image where both, the copper-oxygen-rows along the substrate’s [001] direc-tion can be seen as light blue protrusions, as well as a stacked of chain of about13 DHTAP molecules oriented along the row direction are visible as elongated or-ange protrusions. It is noteworthy that the appearance of the individual DHTAP

34

Section 3.2. DHTAP on Cu(110)-(2x1)O

[110]

[001]

[110]

[110]

Figure 3.19: Cu(110)-(2x1)O from above (left) and from the side (right). The copperatoms are in orange and the oxygen atoms are in red.

Figure 3.20: Detail of a STM image of DHTAP on Cu(110)-(2x1)O. A bending ofthe local densities of states of some molecules is observed, in particular the moleculesmarked with parentheses ”(” and ”)”. The goal of this chapter is to understand theorigin of these features.

35

Chapter 3. Results

molecules varies over the stack of molecules. While some molecules appear straight,indicated by an overlaid vertical bar ”|”, other molecules in the stack appear to bebent as indicated by the other overlaid symbols.

In this thesis we will concentrate on the features marked with parentheses ”(” and”)” and try to answer the following question: is this bending due to an actualphysical bending of the molecule, or are other effects at play?

3.2.2 Adsorption Geometry

First we determine the energetically most favorable adsorption geometry of singleDHTAP molecules on Cu(110)-(2x1)O. We used the rectangular supercell depictedin fig. 3.19 with dimensions of 2

√2aCu ≈ 10.2 A in [110]-direction and 6aCu ≈ 21.6 A

in [001]-direction. Owing to the large intermolecular distances of ∼10.2 A in [110]-direction and ∼7 A in [110]-direction, the molecules can be regarded as isolated inthese calculations.

We considered seven different adsorption sites depicted in Fig. 3.21. For each ofthese adsorption sites we then relaxed the molecule using an ionic relaxation algo-rithm provided by VASP. For the ionic relaxation we used the parameters listed insection A.2. After the relaxation we compared the energies of the different relaxedgeometries.

To this end, we computed the adsorption energy Ead, defined as

Ead = (Emol + Esurf)− Esystem, (3.6)

where Emol is the energy of the isolated molecule, Esurf is the energy of the surfacewithout molecule and Esystem is the energy of the whole system. Since the number ofatoms of the different configurations considered here are the same, we can comparethe energies directly. In addition to the locally relaxed adsorption structure, Fig. 3.21also displays the relative energies ∆E with respect to the most favorable site whichis characterized by a tilted molecule sitting between two Cu-O rows.

The first thing to notice is that in none of the configurations any significant bendingof the molecule is apparent. Closer inspection reveals that configurations where themolecule lies between the oxygen rows are energetically more favorable comparedto configurations where the molecule lies on top of the rows. For instance, compare”O-NH bridge”, ”Hollow” and ”O-N bridge” to ”NH on O”, ”Centre on O” and ”Non O”. Furthermore we see that configurations where the NH groups are close tothe oxygen atoms are energetically favored, compare ”O-NH bridge” and ”NH onO” with the configurations of their respective rows.

The most favorable geometry is the configuration called ”tilted” which is also de-picted in fig. 3.22 in more detail. Here, the molecules are rotated along the longmolecular axis, thus in a side view, the short axis of the molecule makes an anglewith the surface normal, but no significant bending of the molecule is visible. Themolecules moved into the trenches between the oxygen rows, and a strong interactionbetween the N-H group and the oxygen atoms is apparent: in the relaxed geometry,the oxygen atom closest to one of the N-H group is shifted from its equilibriumposition and moved towards the N-H group.

36

Section 3.2. DHTAP on Cu(110)-(2x1)O

TiltedEnergetically favorable

O-NH bridge Hollow O-N bridge∆E = +0.19 eV ∆E = +0.38 eV ∆E = +0.46 eV

NH on O Centre on O N on O∆E = +0.49 eV ∆E = +0.55 eV ∆E = +0.56 eV

Figure 3.21: Table of different adsorption geometries. ∆E is the energy differencebetween a particular configuration and the ”tilted” configuration.

37

Chapter 3. Results

Figure 3.22: ”Tilted” configuration viewed from above (left) and from the side(right). Note in both images the shift of one of the oxygen atoms (in red,markedwith an arrow) towards the N-H group closest to the surface.

Note that in the other six configurations shown in Fig. 3.21, the molecule lies flat onthe surface, thus the short molecular axis is oriented parallel to the surface.

DHTAP-chains

In addition to isolated molecules treated in the previous section, we also calculatedthe adsorption energies for two configurations in which the molecules are closer toeach other, that is one molecule per oxygen row, thereby doubling the coveragecompared to the previous section. For these investigations, the molecules werearranged in the ”tilted” configuration and two adjacent molecules are flipped by 180◦

around the z-axis, such that the pyrazine and dihydro-pyrazine groups of opposingmolecules face each other.

We considered two intermolecular arrangements depicted in Fig. 3.23. In the firstconfiguration depicted in Fig. 3.23a and characterized by the epitaxial matrix(

6 10 2

), (3.7)

adjacent molecules are shifted along the Cu-O row direction leading to a slantedchain of molecules. In the second type of arrangement shown in Fig. 3.23b andcharacterized by the epitaxial matrix(

6 00 2

), (3.8)

a linear chain of stacked molecules result. Energetically, both arrangements arealmost identical (compare Fig. 3.23), where we find only a 20 meV advantage permolecule for the slanted arrangement.

3.2.3 Potential energy surface

In this chapter we aim at the potential energy surface for a diffusion of DHTAPalong the [110] direction. To this end, we perform a large number of fixed-point,

38

Section 3.2. DHTAP on Cu(110)-(2x1)O

(a) Ead/molecule = 2.01 eV (b) Ead/molecule = 1.99 eV

Figure 3.23: Top views of the two different ”chain” configurations. The adsorptionenergies were calculated according to equation 3.6.

Figure 3.24: Visualization of the different parameters changed during one dx-step.dz is the change in height, shown here exaggerated by a factor of ten. dα is theangle increment in each step.

frozen-geometry DFT total energy calculations where the molecular geometry isfrozen in its gas-phase geometry, and the surface atoms are also frozen into theirrelaxed configuration found for the uncovered surface.

We allow for three degrees of freedom which are illustrated in Fig. 3.24 and denotedas dx, dz and dα. They can be characterized as rigid shifts perpendicular to the Cu-O row direction, vertical displacement and as a change of the molecular tilt angle,respectively. Then, starting from the ”NH on O” configuration (c.f. fig. 3.21), weshifted the molecule by dx = 0.5 A increments in the [110] direction. For each shiftwe rotated the molecule about the [001]-direction in dα = 5◦ increments in the rangefrom −35◦ to +35◦ and varied its z-component in dz = 0.1 A increments between−0.2 A and +0.2 A. For each value of dx,dz and dα we then calculated the energyof the configuration.

Thereby, we obtain the three-dimensional potential energy surface E(dx, dz, dα)from which we can extract the minimum energy path for diffusion along the [110]direction. By taking the minimum energy value for each value of dx, we obtainthe energy profile shown in in Fig 3.25. Several conclusions can be drawn fromthe figure. Firstly, the diffusion barrier is in this approximation ≈ 0.35 eV. Itmust be reiterated that the geometry of the molecule was frozen in the gas-phasegeometry. Allowing internal degrees of freedom (bending, twisting of the molecule)would possibly lower this value. Secondly, the energy curve is symmetric with respect

39

Chapter 3. Results

to the dx = 2.5 A point, the potential of the surface is therefore also symmetricaround this point. Thirdly, with increasing dx, the angle of the short axis withthe surface first decreases progressively until the angle reaches its minimum valueof −25◦ at the first minimum point 1.5 A. With increasing dx the angle increasesagain until it reaches its maximum value +25◦. And finally, at the minimum energypoints (dx = 1.5 A and dx = 3.5 A) the center of the molecule is −0.2 A closer tothe surface, thereby increasing the interaction between the N-H group facing thesurface and the closest oxygen atom on the surface.

Another way of representing the potential energy landscape is depicted in fig. 3.26.Here, a two dimensional potential energy map is shown, where for each value of dxand dα, the optimized dz value has been taken. Here, the white curve indicates theoptimal angle for each increment dx in the [110] direction and nicely illustrates howthe molecules vary their tilt angle when diffusing along the [110] direction. Notethat this line quantifies the insets shown at the bottom of fig. 3.25.

3.2.4 Charge rearrangements and workfunction change.

In this subsection, we analyze the electronic structure of the most favorable adsorp-tion geometry, the ”tilted” geometry shown in fig. 3.22,page 38, in more detail. Inparticular, we compute the charge density of the full system ρfull, the charge densityρmolecule of bare DHTAP and the charge density of the surface ρsubstrate. We thencalculated the plane-averaged charge density difference as

∆ρ(z) = ρfull(z)− [ρmolecule(z) + ρsubstrate(z)] (3.9)

and integrated the resulting ∆ρ(z) twice, yielding the change in the electrostaticpotential φ induced by charge rearrangements. The results are plotted in figure3.27.

The grey filled area shows the total charge density given as (number of electrons)/A3.

We can clearly recognize the four layers of copper and half the layer of copper/oxy-gen. The tilted molecule is also clearly visible in the figure, at z ∼ 15 A. Whenanalyzing the charge density difference (red and blue areas), we see that the adsorp-tion of the molecule on the surface depletes the charge density locally (blue area),this visualizes the push-back effect as described in section 2.3. We also see that thecharge density is nowhere increased in the plane of the molecule, showing that thereis no charge transfer into the molecule. This is further corroborated by the pDOSof DHTAP, see fig. 3.28: the LUMO is far above the Fermi energy, therefore no netcharge transfer into the molecule takes place.

The dashed line in figure 3.27 is obtained by integrating ∆ρ(z) twice resulting inthe electrostatic potential change induced by the charge rearrangements upon theadsorption of the molecule. As has been demonstrated in Ref. [32], one can gener-ally separate the workfunction change upon adsorption into three contributions: (i)the workfunction change due to charge rearrangements upon adsorption, called thebonding dipole ∆Φbond; (ii) the workfunction change due to the dipole moment ofthe adsorbed molecule, termed bend dipole ∆Φbend and (iii) finally the workfunctionchange due to substrate-surface buckling.

40

Section 3.2. DHTAP on Cu(110)-(2x1)O

F-F

_min

/ e

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Å

0.0

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0.0

Å

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Å-0.1

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22.5

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44

.55

F-F min / eV

dx / Å

Fig

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41

Chapter 3. Results

Figure 3.26: Energy landscape of the angle. For each dx and optimal dz, the energyof all the different angle increments is color coded, where the minimum energy is inblack. The white line indicates the optimal angle for each dx.

Figure 3.27: Grey: Charge density of the full system. Red (blue): Electron chargeaccumulation (depletion) upon adsorption of the molecule on the surface. Thesecurves are scaled by a factor of 103 for illustrative purposes. Dashed line: Electro-static potential obtained by integrating ∆ρ(z) twice. In this figure we see a strongpush-back effect, manifested by charge depletion (in blue) at the location of themolecule. The vacuum-value of the induced electric potential φ is the workfunctionchange due to the bonding dipole: ∆Φbond ≈ −0.3 eV.

42

Section 3.2. DHTAP on Cu(110)-(2x1)O

L

HH−1H−2

Figure 3.28: PDOS of the ”tilted” geometry. The LUMO, HOMO, HOMO-1, andHOMO-2 peaks are marked with arrows. The LUMO is far above the Fermi energy,indicating that there is no charge transfer into the molecule.

By taking the difference of the electrostatic potential change on both sides of the slab,a value for the bonding dipole ∆Φbond can be extracted. Inspection of the vacuumvalues of the electric potential, we find this bonding dipole to be ∆Φ ∼ −0.3 eV,that is, a reduction of the workfunction of 0.3 eV upon adsorption due to the Paulipush-back effect.

An analysis of the workfunction change using the plane-averaged local electric po-tential shows that the adsorption of the molecule changes the workfunction by−0.33 eV. Furthermore the plane-averaged local potential of a free standing DHTAPmolecule in the ”tilted” geometry reveals a change of −0.02 eV in the electric po-tential due to the dipole moment of the molecule. In summary: the total work-function change ∆Φ ∼−0.33 eV can be divided into the bonding dipole contribu-tion ∆Φbond = −0.30 eV and a bending dipole contribution ∆Φbend = −0.02 eV.Since the total workfunction change is accounted for by the bending and bond-ing dipoles we can infer that the contribution due to substrate-surface buckling isnegligible.

3.2.5 STM-images

Finally, our goal is to understand the appearance of DHTAP molecules on Cu(110)-(2x1)O in experimental STM images such as the one shown in Fig. 3.20, page 35.To this end, we present in this section simulated STM images computed within theTersoff-Haman approximation (see section 2.6) and compare them, where available,to experimental STM images. Note that for all simulated STM images to be shownbelow, the local density of states of the HOMO energy region is depicted, exper-imentally this corresponds to a positive bias voltage applied to the tip: electronstunnel from the molecule into the tip.

43

Chapter 3. Results

Tilted

O-NH bridge Hollow O-N bridge

NH on O Centre on O N on O

Figure 3.29: Table of STM-images of the different adsorption sites. The ordering isthe same as in fig. 3.21. The black circles in each image indicate the position of theoxygen molecules of the surface. In addition, the DHTAP molecule is sketched ineach image.

44

Section 3.2. DHTAP on Cu(110)-(2x1)O

Figure 3.30: Simulated STM image of an isolated DHTAP molecule in the ”tilted”geometry. Here we also observe a bending of the local densities of states.

Constant current STM images of the adsorption sites

The constant current STM images of the seven adsorption sites listed in fig. 3.21(page 37) are tabulated on page 44. We notice that the local density of statesindeed resembles the nodal patterns of the HOMO orbital of DHTAP [40]. At closerinspection, we find that for all flat lying geometries, that is all but the ”tilted”configuration, there is a higher local density of states at the dihydropyrazene sitecompared to the pyrazene site. Interestingly, we observe a ”bending” of the localdensity of state for the ”tilted” geometry. It is important to note that this bendingis not caused by a geometrical bending of the molecule, since the structure of themolecule, albeit tilted towards the surface, remains planar.

In order to investigate the origin for this apparent bending of the molecules in thetilted configuration further, we have also simulated constant current STM imagesfor free standing ”tilted” molecules. For this simulation, we have removed all sur-face atoms in fig. 3.22, while keeping the geometry of the molecule and the sizeof the supercell unchanged. Also this simulated STM image, shown in fig. 3.30,reveals a bent local density of states, suggesting that the observed bending is anintrinsic property of the molecule and not caused by surface-molecule interactions.Presumably it is caused by the presence of the polar groups in DHTAP which, fora tilted arrangement of the molecule, lead to an electrostatic potential landscapewhich bends the local density of states in the manner depicted in Fig. 3.30.

Comparison with experiment

We now compare our simulated STM images for DHTAP on Cu(110)-(2x1)O toexperimental constant current STM images which we kindly received by courtesy ofPeter Zeppenfeld and Conrad Becker [44], see fig. 3.31, page 46.

Remember that for our simulated STM images the intensity is proportional to thelocal density of states of the HOMO, corresponding to a negative bias voltage appliedto the surface. We therefore need to compare our simulated images with the figureon the left, where a negative bias voltage is applied to the surface. In a magnifiedview of a chain of DHTAP molecules, top part of fig. 3.32, the local density of statesappears bent at some points, in particular at the points marked with brackets ”(”and ”)”.

45

Chapter 3. Results

Figure 3.31: Constant current STM images of DHTAO on Cu(110)-(2x1)O. At thebottom of each image the applied bias voltage is shown.

Comparing the ”(” and ”)” parts of the figure with our simulated STM image, asis done in fig. 3.32, we see that theory and experiment are in very good agreement:not only is the local density of states curved as well, but the alignment of thedensity of states with the surface oxygen atoms in the simulated and experimentalSTM images is very similar. Therefore we can conclude that this bending is likelynot due to a structural bending of the molecule itself, but seems to stem from abending of the local density of states, caused by the particular adsorption geometry(”tilted”).

3.2.6 Conclusion

The goal of this chapter was to understand the origin of curved features of availableexperimental STM images of DHTAP on Cu(110)-(2x1)O. In particular, the questionwas raised whether these features arise from a physical bending of the adsorbedmolecules or if other effects are at play.

The first step was to find the optimal adsorption geometry. To this end we put themolecule on different adsorption sites and relaxed the geometries using the molecu-lar dynamics implementation of VASP. The energies were then compared and it wasfound that the ”tilted” geometry is the most favorable geometry. In this geometry,the short axis of the molecule makes an angle with the surface normal, while themolecule is positioned between the oxygen rows. In this geometry, a strong inter-action between the oxygen atoms of the surface and the N-H group of the DHTAPmolecule was found. Furthermore, while the molecule changed position, the moleculegeometry itself was unaltered.

For these relaxed geometries we simulated STM images using the Tersoff-Hamannapproximation. It was found that all except the tilted geometry showed straightlocal densities of states of the HOMO and therefore straight STM features. The

46

Section 3.2. DHTAP on Cu(110)-(2x1)O

Figure 3.32: Detailed comparison between the theoretical and simulated STM im-ages. Top: STM image by courtesy of P. Zeppenfeld and C. Becker [44]. The localdensity of states of DHTAP is shown in orange, the blue rows in the backgroundshow the oxygen atoms of the surface. Bottom: Our simulated STM image of the”tilted” configuration. The oxygen atoms of the surface are marked with black cir-cles. In our simulated STM image the straight side (line ABC) of the local densityof states of the DHTAP molecule is flush with the oxygen rows, while the curvedside (line ADC) is on top of the oxygen rows. This agrees with the experimentalpicture on top: the straight sides (lines ABC) are also flush with the surface oxygenrows, and the curved sides (lines ADC) are on top of the oxygen rows.

tilted geometry on the other hand showed a curved density of states of the HOMO.The HOMO therefore appeared curved in the simulated STM images.

Comparing the simulated STM images with the features marked with ”(” in fig. 3.20,page 35, yielded satisfying results: not only is the local density of states curvedin a similar manner, but the position of the simulated HOMO features relativeto the surface are comparable with the positions of the features marked with ”(”parentheses.

We therefore suggest that the features marked with parentheses ”(” and ”)” infig. 3.20 stem from a curved density of states of the ”tilted” geometry, and not froman actual geometrical bending of the molecule.

47

48

Summary

The goal of this thesis was to investigate two organic/metal interfaces by means ofdensity functional theory. In the first chapter, we investigated tetracene on Ag(110),where we tried to solve an open problem in the interpretation of experimental angle-resolved photoemission data: two measured photoemission momentum maps sepa-rated by ∼ 1 eV both resemble the photoelectron angular distribution expected forthe highest occupied molecular orbital (HOMO). To this end we investigated fourdifferent adsorption geometries of tetracene on Ag(110). From the projected densityof states we could infer that the lowest unoccupied molecular orbitals (LUMO) getspartially filled upon adsorption for all four geometries. The analysis of the workfunc-tion and its change upon tetracene adsorption showed that overall the workfunctionsare lowered for all four geometries, thus the Pauli push-back effect dominates overthe effects arising from the partial charge transfer into the LUMO. For two selectedgeometries (”Huang cell” and ”cross”) we observed an energetic splitting of theHOMO. We simulated angle-resolved photoemission maps and compared them tothe experimental maps denoted as M2 and M3. While the shape of the simulatedphotoelectron angular distributions agreed with the experimental finding, the com-puted energy splitting of ∼0.16 eV for ”Huang cell” and ∼0.08 eV for ”cross” turnedout to be significantly smaller than the measured value. Therefore, a conclusive ex-planation of the experimental findings remains still open.

In the second part we investigated the adsorption of the pentacene derivative Dihydro-tetraaza-pentacene on Cu(110)-(2x1)O. First we determined the optimal adsorptionsite by computing the total energy of different adsorption configurations. We foundthat the so-called ”tilted” geometry, in which the molecules are rotated by 25◦ de-grees around the long molecular axis, is energetically favorable. For this geometrywe calculated the workfunction and workfunction changes and found that the ad-sorption lowers the workfunction by −0.33 eV due to Pauli push-back effect. We alsosimulated the potential energy surface between to adjacent adsorption points in the”frozen geometry” approximation, from which we extracted the diffusion barrier of∼0.35 eV. From the projected density of states we could infer that no charge trans-fer into the molecule takes place and the LUMO resides well above the Fermi level.Finally we simulated STM images for all geometries. Comparing the STM images ofthe ”tilted” geometry with images kindly provided by C. Becker and P. Zeppenfeldproved satisfactory: we could identify one bent feature of the experimental image asoriginating from the local density of states of the ”tilted” geometry and could ruleout any geometric bending of the molecular structure itself.

49

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Appendix A

Computational Details

In this chapter we list the parameters for the performed VASP calculations.

In all calculations, the Tkatchenko-Scheffler method for calculating the dispersionenergy has been used (IVDW=2). Dipole corrections according to [18] are en-abled (LDIPOL=.TRUE.), and the dipole correction is calculated parallel to thez-component of the cell (IDIPOL=3).

The k-points where automatically generated using the Monkhurst-pack.

A.1 Tetracene

INCAR-file:

ISTART = 0NWRITE = 2PREC = AccurateISPIN = 1ISYM = 0ENCUT = 500.0ENAUG = 644.9EDIFF = 5 .E−07EDIFFG = −1E−02NELMIN = 4NSW = 0ISIF = 0IVDW = 2VDW alpha = 15 .4 12 4 .5VDW C6AU = 122 46 .6 6 .5VDW R0 = 1.35 1 .9 1 .64#Atomtype = Ag C HLORBIT = 11EMIN = −10.EMAX = 5 .NEDOS = 1501

55

Appendix A. Computational Details

ISMEAR = 1SIGMA = 0.10LREAL = AVOSKOWN= 1ALGO = FLDIAG = .TRUE.LPLANE = .TRUE.NSIM = 4NPAR = 4LWAVE = .TRUE.LCHARG = .TRUE.LVHAR = .TRUE.IDIPOL = 3LDIPOL = .TRUE.

KPOINTS-file:

automatic mesh0

Monkhurst3 3 1

0 0 0

List of used pseudopotentials:

PAW PBE Ag 02Apr2005TITEL = PAW PBE Ag 02Apr2005

PAW PBE C 08Apr2002TITEL = PAW PBE C 08Apr2002

PAW PBE H 15Jun2001TITEL = PAW PBE H 15Jun2001

For molecular relaxations, the following parameters have been used:

EDIFFG = −1E−02NELMIN = 4NSW = 200IBRION = 3POTIM = 0.15SMASS = 0.4

The number of steps (NSW) was adjusted if necessary.

A.2 DHTAP

INCAR-file:

NCORE = 16ISTART = 0NWRITE = 2

56

Section A.2. DHTAP

PREC = AccurateISPIN = 1ISYM = 1ENAUG = 644.9EDIFF = 5 .E−05ISIF = 0IVDW = 2VDW ALPHA = 12 4 .5 7 .4 10 .9 5 .4VDW C6AU = 46.6 6 .50 24 .2 59 15 .6VDW R0 = 1.9 1 .64 1 .77 1 .27 1 .69#Atomtype = C H N Cu OLORBIT = 11EMIN = −10.EMAX = 5 .NEDOS = 1501ISMEAR = 1SIGMA = 0.20LREAL = AVOSKOWN= 1ALGO = FLDIAG = .TRUE.LPLANE = .TRUE.NSIM = 4NPAR = 4LWAVE = .FALSE.LCHARG = .FALSE.LVHAR = .FALSE.IDIPOL = 3LDIPOL = .TRUE.

KPOINTS-file:

automatic mesh0

Monkhurst4 2 1

0 0 0

List of used pseudopotentials:

PAW PBE C 08Apr2002TITEL = PAW PBE C 08Apr2002

PAW PBE H 15Jun2001TITEL = PAW PBE H 15Jun2001

PAW PBE N 08Apr2002TITEL = PAW PBE N 08Apr2002

PAW PBE Cu 22Jun2005TITEL = PAW PBE Cu 22Jun2005

PAW PBE O 08Apr2002TITEL = PAW PBE O 08Apr2002

57

Appendix A. Computational Details

For molecular relaxations, the following parameters have been used:

EDIFFG = −1E−02NELMIN = 4NSW = 0IBRION = 3POTIM = 0.15SMASS = 0.4

The number of steps (NSW) was adjusted if necessary.

58

Appendix B

Kohn-Sham Orbitals of Tetracenein the Gas Phase

For tetracene in the gas phase visualizations of the Kohn-Sham orbitals and simu-lated ARPES-maps of the LUMO, HOMO, HOMO-1 and HOMO-2 are available.Here we tabulate them for reference.

59

Appendix B. Kohn-Sham Orbitals of Tetracene in the Gas Phase

LUMO

HOMO

HOMO-1

HOMO-2

Figure B.1: Kohn-Sham orbitals (left column) and simulated ARPES-maps (rightcolumn) for tetracene in the gas phase.

60